Suppose that 20 students take a statistics exam worth 100 points. The standard deviation of the exam scores is 5 points.
Which one of the following statements gives the most reasonable description of the distribution of exam scores?
To determine the most reasonable description of the distribution of exam scores, we need to consider the information provided.
The standard deviation is a measure of dispersion or spread in a distribution. In this case, the standard deviation is given as 5 points. A smaller standard deviation indicates less variability or spread in the scores, whereas a larger standard deviation indicates more variability or spread.
Based on this information, we can analyze the given statements to determine the most reasonable description of the distribution of exam scores. Here are the options:
1. All scores are clustered around the mean.
2. Some scores are above the mean, some are below, and most are clustered around the mean.
3. All scores are equal to the mean.
4. Scores are evenly dispersed around the mean.
Given the standard deviation of 5 points, the statement that best describes the distribution of exam scores is option 2: "Some scores are above the mean, some are below, and most are clustered around the mean."
Explanation for getting the answer:
To determine the most reasonable description, we use our understanding of statistics and the concept of standard deviation. A standard deviation of 5 points suggests that there is some variability in the scores. Hence, it is reasonable to expect that some scores would be above the mean, some below the mean, and the majority of the scores clustered around the mean. This would indicate a distribution with some spread but a tendency for scores to be centered around the mean.